In an A.P. if `S_1=T_1+T_2+T_3+.....+T_n(nod d)dotS_2=T_2+T_4+T_6+.........+T_(n-1)` , then find the value of `S_1//S_2` in terms of `ndot`

If int_0^1(e^t)/(1+t)dt=a , then find the value of int_0^1(e^t)/((1+t)^2)dt in terms of a .

For an A.P., if a = -3 and d = 4 then find t_n

Let T_r denote the rth term of a G.P. for r=1,2,3, If for some positive integers ma n dn , we have T_m=1//n^2 and T_n=1//m^2 , then find the value of T_(m+n//2.)

If T_0,T_1, T_2,.....T_n represent the terms in the expansion of (x+a)^n , then find the value of (T_0-T_2+T_4-....)^2+(T_1-T_3+T_5-.....)^2n in Ndot

Find the locus of the point (t^2-t+1,t^2+t+1),t in Rdot

If p(t)=t^(3)-1 , find the values of p(1),p(-1),p(0),p(2),p(-2) .

If t_(n)" is the " n^(th) term of an A.P. then the value of t_(n+1) -t_(n-1) is ……

In an A.P. with first term 'a' and common difference 'd' t_(2n) - t_(n) is : (where t_(n) " is the " n^(th) term )

Consider two A.P. s: S_1:2,7,12 ,17 , 500t e r m s a n dS_1:1,8,15 ,22 , 300t e r m s Find the number of common term. Also find the last common term.